On the topology of topological fundamental groupoids
[EN] This paper is devoted to the Lasso and the Whisker topology of the fundamental groupoid. We prove that topological fundamental groupoid of a given space X is locally path connected in general and is path connected if X is simply connected. We show that for locally path connected space...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/221860 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/221860 |
| Access Level: | acceso abierto |
| Palabra clave: | Topological fundamental groupoid Lasso topology Whisker topology |
| Sumario: | [EN] This paper is devoted to the Lasso and the Whisker topology of the fundamental groupoid. We prove that topological fundamental groupoid of a given space X is locally path connected in general and is path connected if X is simply connected. We show that for locally path connected space X, the unit map 1 : X → π X is an embedding if and only if X is a semilocally simply connected space. Also, we give conditions that guarantee Hausdorffness of the topological fundamental groupoid. |
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